The fact that linear equalizers have been the focus of a great deal of research in the past several decades is well justified when one considers their simple nature and adequate performance over well-behaved channels. Similarly, decision feedback equalizers (DFE) have also enjoyed practical success due to their simplicity and their ability, unlike linear equalizers, to perform well over channels with spectral nulls. These conclusions are well documented by Qureshi in reference 2! and Proakis in reference 3!.
In order to track channel variations, equalizers may operate in a continuously adaptive mode, albeit with significant computational burden as was shown by G. W. Davidson et al. in reference 4!. One method of alleviating the overhead of continuous adaptation is to adapt the equalizer coefficients periodically based on a known training sequence. One problem with this and other practical schemes, however, is that due to channel fluctuations, the receiver is not always optimized for the actual channel, i.e., channel mismatch occurs.
Although the practical importance of channel mismatch warrants theoretical analyses, there are relatively few references which formally address this topic. In his doctoral thesis, Divsalar 5! investigated the impact of channel mismatch on maximum-likelihood (ML) receivers and derived bounds on the error-event probability. Although his analysis imposed few restrictions on the type of channel mismatch, the ML-based formulation does not lend itself to linear or DFE receivers.
A brief analysis which was conducted for linear equalizers in magnetic recording applications is developed in the work of D. G. Messerschmitt et al. 6!. However, due to the narrow scope of their analysis, their particular results do not lead to a simple and broadly applicable implementation.
In a patent by Gurcan in reference 1!, a method was described which attempts to optimize the peak reference tap of a DFE in order to optimize its MSE performance. In addition, it was assumed by Gurcan in reference 1! that increasing the number of feed-forward taps could improve performance. While this may be possible under ideal conditions, my results show that this is not always valid under severe channel mismatch conditions.
Other equalizer references such as Davidson et al. 4! and Bingham 7! have resorted to computer simulation to obtain useful performance predictions for equalizers. Indeed, it is evident from the literature that this kind of computer simulation has been a (and perhaps the only) practical means of ascertaining the sensitivity of complex receivers to channel mismatch. However, the computational requirements incurred by these simulations may be quite significant.
Thus, it is clear that existing performance estimators either grossly bound the MSE (by simply ignoring the channel mismatch) or calculate it via cumbersome analyses and/or expensive Monte Carlo simulation techniques, which are not amenable to real-time applications. Therefore, although there are performance estimators which may be of use assuming ideal (no mismatch) conditions, there are no low-cost methods of quickly estimating equalizer performance under arbitrary channel mismatch conditions. The present system and method provides such a solution.